Winter School 2012

Todd Eisworth, Stefan Geschke, K. P. Hart, István Juhász

Program

This year of the tutorial lectures (each tutorial comprising of several 50 minute lectures) were devoted to advanced topics of Set Theory & Set-Theoretic topology. They were delivered by leading experts in the respective fields.

Professor Todd Eisworth (Ohio University, Athens OH) gave a series of talks on the reflection and nonreflection of stationary sets at successors of singular cardinals.

Professor Stefan Geschke (Hausdorff Center for Mathematics, Bonn) gave a tutorial on the topic of definable colorings of graphs and related cardinal invariants.

Professor K. P. Hart (Delft University of Technology, Delft) had a series of lectures showing some applications of the Lowenheim-Skolem theorem to the lattice of closed sets of compact spaces.

Professor István Juhász (Alfréd Rényi Institute of Mathematics, Budapest) talked about resolvability of topological spaces and presented recent developments in the field.

The research presentations were given mainly by younger participants who presented their newest results. The topics included General Topology, Set Theory, Boolean Algebras and Forcing, Descriptive Set Theory, Large Cardinals and the Theory of Ultrafilters.

Each day participants had time to discuss their work with colleagues. The topics of the discussions were diverse and included recent developments in set theory.

Participants

Giorgio Audrito, Bohuslav Balcar, Taras Banakh, Artur Bartoszewicz, Wojciech Bielas, Marek Bienias, Piotr Borodulin-Nadzieja, Gemma Carotenuto, David Chodounsky, Michal Dečo, Natasha Dobrinen, Todd Eisworth, Peter Eliaš, Ahmad Farhat, Barnabás Farkas, Jana Flašková, Stefan Geschke, Szymon Glab, Klaas Pieter Hart, Rodrigo Hernandez Gutierrez, Fernando Hernandez-Hernandez, Radek Honzík, István Juhász, Alicja Krzeszowiec, Wieslaw Kubiś, Andrzej Kucharski, Marta Nowakowska, Aleksandar Pavlović, Tomáš Pazák, Grzegorz Plebanek, Szymon Plewik, Robert Ralowski, Edoardo Rivello, Růžena Roháčková, Jeff Serbus, Petr Simon, Lajos Soukup, Wojciech Stadnicki, Jan Stary, Carsten Szardenings, Katie Thompson, Boris Šobot, Jaroslav Šupina, Egbert Thuemmel, Fabio Tonti, Jonathan Verner, Anna Vernerová, Zoltan Vidnyanszky, Mate Vizer, Marta Walczyńska, Thilo Weinert, Marek Wyszkowski, Teruyuki Yorioka, Szymon Zeberski

Photos

Talks, slides, abstracts

SpeakerTitleAbstract/Slides
Jaroslav ŠupinaSpaces not mappable onto [0,1] slides
Taras BanakhSolecki submeasures and densities on groups
Marek BieniasIndependent Bernstein sets and algebraic constructions slides
Natasha DobrinenRamsey-classification theorems and applications in the Tukey theory of ultrafilters slides / paper
Todd EisworthSuccessors of Singular Cardinals I.
Todd EisworthSuccessors of Singular Cardinals II. slides
Todd EisworthSuccessors of Singular Cardinals III. slides
Peter EliašPermitted sets on Cantor group slides
Ahmad FarhatLocal connectedness and images of βH* slides
Barnabás FarkasCovering properties of ideals slides
Jana FlaškováThe generic existence of certain I-ultrafilters slides
Stefan GeschkeDefinable graphs on Polish spaces I. slides
Stefan GeschkeDefinable graphs on Polish spaces II. slides
Stefan GeschkeDefinable graphs on Polish spaces III. slides
Szymon Glabstrong algebrability of series and functions slides
Klaas Pieter HartApplications of the Löwenheim-Skolem theorem to compact hausdorff spaces I. slides
Klaas Pieter HartApplications of the Löwenheim-Skolem theorem to compact hausdorff spaces II. slides
Klaas Pieter HartApplications of the Löwenheim-Skolem theorem to compact hausdorff spaces III. slides
Rodrigo Hernandez GutierrezCountable Dense Homogeneous Filters slides / paper
Radek HonzíkSupercompact cardinals and failures of GCH slides
István JuhászResolvability of topological spaces I. slides
István JuhászResolvability of topological spaces II. slides
István JuhászResolvability of topological spaces III. slides
Wieslaw KubiśUniversal homogeneous structures in ZFC slides
Grzegorz PlebanekSimple Boolean algebra with complicated space of measures slides
Szymon PlewikKatowice ”pattern” for the questions inspired by Czech mathematicians slides
Robert RalowskiTwo-point sets slides
Lajos SoukupVariations of Separability slides
Jan StaryCoherent ultrafilters on Boolean algebras slides
Egbert ThuemmelThe Horn-Tarski problem slides / paper
Zoltan VidnyanszkyCoanalytic Transfinite Constructions slides
Marta WalczyńskaKuratowski operations revisited slides
Thilo WeinertTransfinite ordinal partition relations and coloured finite digraphs slides
Marek WyszkowskiThe independence of the covering numbers of the ideals of splitting tree forcing and Sacks forcing slides
Teruyuki YoriokaSome results in the extension with a coherent Suslin tree slides
Teruyuki YoriokaKilling some S-spaces by a coherent Suslin tree slides
SpeakerTitleAbstract/Slides
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